A local school board is conducting a study of the growth in student enrollment in its schools. this growth can be modeled by the function f(t)=5230(1.015)t, where t represents the number of years since the study began. which function can be used to represent the student enrollment m months after the study began?

Answer:

It could be any of them.

Step-by-step explanation:

First off, It could be said that (2c-d)(2c-d) doesn't belong because it includes two subtractions signs and none of the others do.

Secondly, It could be said that (2c+d)(2c-d) doesn't belong because it includes one subtraction sign and one addition sign and none of the others do.

Thirdly, It could be said that (2c+d)(2c+d) doesn't belong because it includes two addition signs, and none of the others do.

Finally, it could be said that (c+d)(c+d) doesn't belong because it doesn't have a multiplying factor of 2 within the parentheses.

I hope this helps :)

Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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The probability that at most 5 of these lights are red is 0.971.

To calculate this probability, we can use the binomial distribution with n = 7 and p = 0.4, since we want to know the probability of getting at most 5 red lights out of 7. We can use the formula:

P(X ≤ 5) = ΣP(X = k) for k = 0 to 5

Using this formula, we can calculate the probability as follows:

P(X = 0) = (0.5)^7 = 0.0078

P(X = 1) = 7(0.5)^7 = 0.0547

P(X = 2) = 21(0.4)(0.6)^6 = 0.2028

P(X = 3) = 35(0.4)^2(0.6)^5 = 0.322

P(X = 4) = 35(0.4)^3(0.6)^4 = 0.2458

P(X = 5) = 21(0.4)^4(0.6)^3 = 0.0907

Therefore, the probability of getting at most 5 red lights out of 7 is:

P(X ≤ 5) = 0.0078 + 0.0547 + 0.2028 + 0.322 + 0.2458 + 0.0907 = 0.971.

So the probability that at most 5 of these lights are red is 0.971.

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The surface area of the rectangular prism figure is S = 838 cm²

Given data ,

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

So, the value of S is given by

The heights of the prism is represented as 7cm.

S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )

On simplifying the equation , we get

S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60

S = 838 cm²

Therefore , the value of S is 838 cm²

Hence , the surface area is S = 838 cm²

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Answer:

Step-by-step explanation:

y = x + 8

x + y = 2

using substitution, since y is equal to x + 8 we substitute it for the y in x + y = 2

so we get: x + (x+8) =2

then we simplify, getting 2x + 8 = 2

We make the x on its own on one side of the equation by subtracting 8 on both sides.

2x = -6

divide

x = -3

y = 5

(if x = -3, y = 5 because -3 + 8 =5)

test answer

5 = -3 + 8 works and -3 + 5 = 2 works as well

Answer:

$39 per square foot.

Step-by-step explanation:

The cylinder has a height of 2 feet and a radius of 5 feet.

The total cost of the metal will be (assuming US dollars) $8572.20.

And we want to determine the cost per square foot.

First, we can find the surface area of the cylinder. The surface area for a cylinder is given by the formula:

\(SA=2\pi r^2+2\pi rh\)

Where r is the radius and h is the height.

Since the radius is 5 feet and the height is 2 feet and using 3.14 for π, the surface area is:

\(SA=2(3.14)(5)^2+2(3.14)(5)(2) =219.8\text{ feet}^2\)

Therefore, to find the cost of metal per square foot, we can divide the total cost over the amount of surface area. Hence:

\(8572.20 / 219.8= \$ 39 \text{ per square foot}\)

So, the metal costs $39 per square foot.

Answer:

x=26°, y=26°, z=26°

Step-by-step explanation:

x+74=100 (the sum of linear pair)

x=100-74

x=26

x=y=26 (alternate angle)

y=z=26 (vertically opposite angle V.O.A)

Answer:

Option (2)

Step-by-step explanation:

If the first term of an arithmetic sequence is 'a' and common difference as 'd',

Explicit formula representing the nth term of the sequence is given by,

\(a_n=a+(n-1)d\)

Here, n = number of term

If first term 'a' = 19 and common difference 'd' = 4

Explicit formula for the sequence will be,

\(a_n=19+(n-1)4\)

Therefore, Option (2) will be the correct option.

Answer: 100 + (20 x W)

Step-by-step explanation:

100 is the money that is already in the account so it will just be added to what she saves afterward. W stands for the weeks she saves, which will be multiplied by 20 since it is what she will save per week.

(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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True, we can compare a model before using a transformation on x or y to a mode before using a transformation by using the corresponding values of the sum of squares error SSE.

      For example, to compare two models, one of which has a transformation on the outcome of the variable, that is:

First model\(y=x+z\)

Second model:\(y^{1/k} =x+z\)

The best logical approach might be to look at the comparative performance obviously with predicted transformed values back-transformed and then look at the models sum of squares error of these predictions. It has to be random predictions and comparisons because the error distributions are also transformed.

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Answer:

undefined

Step-by-step explanation:

slope = change in y / change in x

Let's take change as (second point) - (first point). We could do (first point) - (second point), but we have to choose one

slope = (y₂-y₁)/(x₂-x₁)

          = (7/7)/(0)

           = 1/0

Anything divided by 0 is undefined, so the line has no slope/is undefined

Before the beginning of the Korean War, Kim II-Sung had established his plans to invade South Korea and shared them with Soviet Union and China.

To be able to spread communist ideologies across the neighboring countries, Kim II-Sung planned to invade South Korea for the same.

Soviet Union and China also joined hands, as they were also focused on wide-spreading the communal ideologies throughout the world.

Hence, it may be stated that the invasion of South Korea took place for spreading communism.

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Answer:

1. Kim Il-Sung was the leader of

✔ North Korea.

2. Before the war, Kim Il-Sung informed the Soviet Union and China of his plan to invade

✔ South Korea.

3. The South Korean government was led by President

✔ Syngman Rhee.

4. South Korea’s leadership arrested and killed thousands of

✔ alleged North Korean agents.

Step-by-step explanation:

The estimated cost savings for the homeowner in a year if she replaces refrigerator A with refrigerator B would be $72.

To calculate the cost savings, we first need to calculate the annual electricity cost for refrigerator A, which is 500 watts/hour * 12 hours/day * 365 days/year = 2,190,000 watt-hours/year or 2190 kWh/year. Multiplying this by the cost per kWh of $0.12 gives us an annual electricity cost of $262.80.

For refrigerator B, which uses 50% less energy per year, the annual electricity cost would be 2190 kWh/year * 0.5 * $0.12/kWh = $131.40. Therefore, the estimated cost savings for the homeowner in a year would be $262.80 - $131.40 = $131.40. However, the cost savings over the lifespan of the refrigerator will depend on its lifespan, replacement cost, and future changes in energy prices.

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Answer:

NO

Step-by-step explanation:

Answer:

No!!

Step-by-step explanation:

just... no.

The greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

Percentage is a number or ratio expressed as a fraction of 100.

We can calculate the percent change between two values using the following formula:

percent change = (new value - old value) / old value x 100%

To compare the percent change over a five-year period, we need to consider the percent change between each pair of values, as follows:

Percent change between the first and second year:

percent change = (320 - 200) / 200 x 100% = 60%

Percent change between the second and third year:

percent change = (400 - 320) / 320 x 100% = 25%

Therefore, the greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

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Discount is 0.354838, Discount percentage is 35.4838 %.

According to the question

A shop item is marked down from r 6.20 to r 4.

A discount is an amount that is subtracted from the regular price of an item.

Based on the given conditions

= \(\frac{6.2-4}{6.2}\)

Solving 6.2 - 4, we get 2.2

= 2.2/6.2

Discount = 11/31 = 0.354838

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred. For example, a percentage discount of 20% would mean that an item that originally cost $100 would now cost $80.

Discount percentage = \(\frac{11}{31}\) × 100

= 35.4838 %

Hence,

Discount is 0.354838, Discount percentage is 35.4838 %.

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Answer:

3

Step-by-step explanation:

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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The required distance  Lacy walks 0.6 kilometers or 600 meters.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

We can start by assigning a variable to the number of kilometers that Lacy walks. Let's use "L" for Lacy's distance.

Since Emma walks 5.4 kilometers farther than Lacy, we can express

Emma's distance in terms of Lacy's distance as:

E = L + 5.4

where "E" represents Emma's distance.

If Emma walks 6 kilometers, we can set E equal to 6 and solve for L:

E = L + 5.4

6 = L + 5.4

Subtracting 5.4 from both sides, we get:

0.6 = L

So Lacy walks 0.6 kilometers or 600 meters.

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The statement is false. Two matrices can be multiplied only if the number of columns in the first matrix matches the number of rows in the second matrix.

The given statement is incorrect. Matrix multiplication requires a specific condition: the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. The entries of the resulting matrix are obtained by taking the dot product of each row of the first matrix with each column of the second matrix. Therefore, it is not necessary for the two matrices to have the same number of entries, but rather they need to satisfy the condition mentioned above.

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Answer:

1 +6 x + 12 x 2 + 8x 3

Explanation:

We must use our knowledge of the binomial expansion:

Method 1:

We can use:

(

x

+

1

)

n

=

1

+

n

x

+

n

(

n

−

1

)

2

!

x

2

+

n

(

n

−

1

)

(

n

−

2

)

3

!

x

3

+

...

Substituting  

n

=

3

and  

x

for  

2

x

⇒

(

2

x

+

1

)

3

=

1

+

(

3

⋅

2

x

)

+

3

⋅

2

2

!

⋅

(

2

x

)

2

+

3

⋅

2

⋅

1

3

!

⋅

(

2

x

)

3

=

1

+

6

x

+

12

x

2

+

8

x

3

Method 2:

We can use:

(

A

+

B

)

n

=

A

n

+

(

n

1

)

A

n

−

1

B

1

+

(

n

2

)

A

n

−

2

B

2

+

...

Letting  

A

=

2

x

and

B

=

1

for this circumstance:

(

2

x

+

1

)

3

=

(

2

x

)

3

+

(

3

1

)

(

2

x

)

2

(

1

)

+

(

3

2

)

(

2

x

)

1

(

1

)

2

+

(

3

3

)

(

2

x

)

0

(

1

)

3

=

8

x

3

+

12

x

2

+

6

x

+

1

Step-by-step explanation:

Answer: Z<4

Step-by-step explanation:

Rearrange the equation

-3(z-6) - (2z-2)>0

-3z+18-2z+2>0

-5z +20>0

-5(z-4)>0

divide  both side by -5

z-4<0

z<4

Answer:

-The increase in dollars is $1598

-The amount in her account at the end of last year was $8398.

Step-by-step explanation:

To find the increase, you have to multiply the initial amount for the percentage increase:

6800*23.5%=1598

Now, to find the amount in her account at the end of last year, you have to add the initial amount plus the increase in dollars:

6800+1598=8398

According to this, the amount in her account at the end of last year was $8398.

Answer:

  (c)  the converse of the original conditional statement

Step-by-step explanation:

If a conditional statement is described by p→q, you want to know what is represented by q→p.

For the conditional p→q, the variations are ...

As you can see from this list, ...

  the converse of the original conditional statement is represented by q→p, matching choice C.

__

Additional comment

If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.

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The total cost of the fence, rounded to the nearest pound, is £656.

To calculate the total cost of the fence, we need to find the perimeter of the right-angled triangle-shaped field. The perimeter is the sum of the lengths of all three sides.

Given that the field has a right angle and one angle measures 52°, we can use trigonometry to determine the lengths of the sides.

Let's denote the lengths of the sides as follows:

The side opposite the 52° angle as a

The side adjacent to the 52° angle as b

The hypotenuse (the longest side) as c

Using trigonometric ratios, we have:

tan(52°) = a / b

Rearranging the equation, we get:

a = b * tan(52°)

We also know the length of side b is 151 m.

Plugging in the values, we find:

a = 151 * tan(52°) ≈ 118.63 m

Now, we can calculate the hypotenuse c using the Pythagorean theorem:

c = √(a^2 + b^2) = √(118.63^2 + 151^2) ≈ 193.17 m

The perimeter of the triangle is the sum of the three sides:

Perimeter = a + b + c ≈ 118.63 + 151 + 193.17 ≈ 462.8 m

Finally, to calculate the total cost of the fence, we multiply the perimeter by the cost per meter:

Total cost = Perimeter * Cost per meter = 462.8 * £1.42 ≈ £656.34

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Answer:

B.) 154 feet

Step-by-step explanation:

i got it right on edge    

\(hope that helps\)